Non-isomorphic 2-groups with isomorphic modular group algebras

Diego García-Lucas, Leo Margolis, Ángel del Rı́o

2021Journal für die reine und angewandte Mathematik (Crelles Journal)18 citationsDOI

Abstract

Abstract We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

Topics & Concepts

Isomorphism (crystallography)Modular designMathematicsGroup (periodic table)Pure mathematicsGroup isomorphismField (mathematics)Algebra over a fieldAutomorphismComputer scienceAutomorphism groupPhysicsChemistryOuter automorphism groupCrystallographyQuantum mechanicsOperating systemCrystal structureFinite Group Theory ResearchCoding theory and cryptographyRings, Modules, and Algebras